Elliptic curve isogeny class 567.5-f over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-567.5-f
• Conductor: 567.5
• Rank: \( 1 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 567.5-f over \(\Q(\sqrt{7}) \)

Isogeny class 567.5-f contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
567.5-f1	\( \bigl[0\) , \( a - 1\) , \( a\) , \( -44 a - 112\) , \( 230 a + 605\bigr] \)
567.5-f2	\( \bigl[0\) , \( a - 1\) , \( a\) , \( 96 a + 258\) , \( 1380 a + 3648\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph